Problem: Rewrite as a simplified fraction. ${3.37\overline{3} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3373.3333...\\ 100x &= 337.3333...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3036}$ ${x = \dfrac{3036}{900}} $ ${x = \dfrac{253}{75}} \text{or} {3 \dfrac{28}{75}}$